Question

A cylinder of mass $20kg$ is immersed in the water. It weighs $8kg$ in the water. If the area of cross-section is $5m^2$, then find out the length of cylinder.
(Density of water (${\rho }_w$)$=1000kg{m}^{-3},g=10m{s}^{-2}$)

• A. $1.4cm$
• B. $2.4cm$
• C. $1.2mm$
• D. $2.4mm$

Answer 1

The correct option is D $2.4mm$

Given:
Mass of cylinder $M$$=20kg$
Apparent weight of cylinder in water,
$M_w$$=8kg$
Area of cylinder, $A=5m^2$
Density of water (${\rho }_w$)$=1000kg{m}^{-3}$
Let's assume the length of cylinder$=l$
Volume of cylinder $=V$
Loss of weight in water of cylinder, $=M-M_w=20-8=12kg$

We know that,
According to Archemedes' Principle loss in weight of body in the water is equal to the weight of displaced water by the body.

$(M-M_w)\times g=\left(V{\rho }_w\right)\times g$
$12=A\times l\times 1000$
$12=5\times l\times 1000$
$l=\frac{12}{5000}=0.0024m=2.4mm$